Statistics question

Question

The credit department of Lion’s Department Store in Anaheim, California, reported that 30% of their sales are cash, 24% are paid with a credit card, and 46% with a debit card. Twenty percent of the cash purchases, 84% of the credit card purchases, and 57% of the debit card purchases are for more than $50.

Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash?

Answer 1

1.) We need to find the probability of buying items more than $50 with cash only.

P(Cash and Amount > $50) = (0.30)(0.20) = 0.06

2.) We need to find the probability of buying items more than $50 with either cash, credit card, and debit card.

P(Amount > $50) = (0.30)(0.20) + (0.24)(0.84) + (0.46)(0.57) = 0.5238

3.) We need to find the probability that Tina paid with cash given that her purchase is more than $50.

P(Cash | Amount > $50) = 0.06/0.5238 = 0.115